question_answer

A person standing on the bank of a river observes that the angle of elevation of the top of a tree on the opposite bank of the river is \[{{60}^{o}}\] and when he moves 40m away from the tree, the angle of elevation becomes \[{{30}^{o}}\]. The breadth of the river is

A)  20 m                           

B)  30 m

C)  40 m                           

D)  60 m

Correct Answer: A

Solution :

Let height of tree = x In \[\Delta ABC,\] \[\frac{h}{x}=\tan {{60}^{0}}\Rightarrow \,h=\sqrt{3}x\] In \[\Delta ABD,\] \[\frac{h}{x+40}\tan {{30}^{0}}\] \[\Rightarrow \,\,\sqrt{3}h\,=x+40\] \[\therefore \] From (1) and (2), we get x = 20m.